18.755 Introduction to Lie Groups (MIT)
This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric
Author(s): Helgason, Sigurdur

21F.019 Communicating Across Cultures (MIT)
It has become commonplace knowledge that globalization is one of the major forces shaping our world. If we look at the spread of information, ideas, capital, media, cultural artifacts - or for that matter, people - we can see the boundaries and borders that have historically separated one country or one group from another are becoming more and more permeable. For proof of this close to home, you need only to look at the composition of the MIT student body: 8 percent of the undergraduates an
Author(s): Widdig, Bernd,Breslow, Lori

Classroom Innovations through Lesson Study
Classroom Innovations through Lesson Study is an APEC EDNET Project that aims to improve the quality of education in the area of Mathematics. This project is sponsored by APEC Members Japan and Thailand. The APEC-Tsukuba International Conference III was broadcast live from Tokyo, December 9-10, 2007. The project has produced useful papers describing mathematical thinking, lesson videos of classroom instruction. This project focuses on Lesson Study with the goal of improving the quality of educat
Author(s): No creator set

Introduction to Nanoscale Science: Surface Area to Volume Ratio Module
Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale
Author(s): No creator set

MAS.450 Holographic Imaging (MIT)
MAS.450 is a laboratory course about holography and holographic imaging. This course teaches holography from a scientific and analytical point of view, moving from interference and diffraction to imaging of single points to the display of three-dimensional images. Using a "hands-on" approach, students explore the underlying physical phenomena that make holograms work, as well as designing laboratory setups to make their own images. The course also teaches mathematical techniques that allow the b
Author(s): Halle, Michael,Benton, Stephen

Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey
Author(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 2. Are You Convinced?
Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give
Author(s): Harvard-Smithsonian Center for Astrophysics

The Great Magnet, the Earth
This site provides a non-mathematical introduction to the magnetism of the Earth, the Sun, the planets and their environments, following a historical thread. In 1600, four hundred years ago William Gilbert, later physician to Queen Elizabeth I of England, published his great study of magnetism, "De Magnete"--"On the Magnet". It gave the first rational explanation to the mysterious ability of the compass needle to point north-south: the Earth itself was magnetic. "De Magnete" opened the era of mo
Author(s): No creator set

I am finding my students are increasingly using spreadsheets to solve mathematical problems in class and represent their data and findings in meaningful ways.  Th
Author(s): Creator not set

18.238 Geometry and Quantum Field Theory (MIT)
Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.
Author(s): Etingof, Pavel

15.075 Applied Statistics (MIT)
This course is an introduction to applied statistics and data analysis. Topics include collecting and exploring data, basic inference, simple and multiple linear regression, analysis of variance, nonparametric methods, and statistical computing. It is not a course in mathematical statistics, but provides a balance between statistical theory and application. Prerequisites are calculus, probability, and linear algebra. We would like to acknowledge the contributions that Prof. Roy Welsch (MIT), Pro
Author(s): Newton, Elizabeth

STS.035 The History of Computing (MIT)
This course focuses on one particular aspect of the history of computing: the use of the computer as a scientific instrument. The electronic digital computer was invented to do science, and its applications range from physics to mathematics to biology to the humanities. What has been the impact of computing on the practice of science? Is the computer different from other scientific instruments? Is computer simulation a valid form of scientific experiment? Can computer models be viewed as surroga
Author(s): Gerovitch, Slava

18.413 Error-Correcting Codes Laboratory (MIT)
This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the dec
Author(s): Spielman, Daniel

18.305 Advanced Analytic Methods in Science and Engineering (MIT)
Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.
Author(s): Cheng, Hung

8.591J Systems Biology (MIT)
This course introduces the mathematical modeling techniques needed to address key questions in modern biology. An overview of modeling techniques in molecular biology and genetics, cell biology and developmental biology is covered. Key experiments that validate mathematical models are also discussed, as well as molecular, cellular, and developmental systems biology, bacterial chemotaxis, genetic oscillators, control theory and genetic networks, and gradient sensing systems. Additional specific t
Author(s): van Oudenaarden, Alexander

6.881 Representation and Modeling for Image Analysis (MIT)
Most algorithms in computer vision and image analysis can be understood in terms of two important components: a representation and a modeling/estimation algorithm. The representation defines what information is important about the objects and is used to describe them. The modeling techniques extract the information from images to instantiate the representation for the particular objects present in the scene. In this seminar, we will discuss popular representations (such as contours, level sets,
Author(s): Golland, Polina

6.435 System Identification (MIT)
This course is offered to graduates and includes topics such as mathematical models of systems from observations of their behavior; time series, state-space, and input-output models; model structures, parametrization, and identifiability; non-parametric methods; prediction error methods for parameter estimation, convergence, consistency, and asymptotic distribution; relations to maximum likelihood estimation; recursive estimation; relation to Kalman filters; structure determination; order estima
Author(s): Dahleh, Munther

18.091 Mathematical Exposition (MIT)
This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.
Author(s): Carberry, Emma

14.12 Economic Applications of Game Theory (MIT)
Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on the behavior of other agents. It involves the analysis of conflict, cooperation, and (tacit) communication. Game theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of game theory, pr
Author(s): Yildiz, Muhamet

9.29J Introduction to Computational Neuroscience (MIT)
This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley and other related models of neural excitability, stochastic models of ion channels, cable theory, and models of synaptic transmission. Visit the Seung Lab Web s
Author(s): Seung, Sebastian